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Sometimes I really get curious and want to know about something.
I haven't seen the Ham Radio article, but I'm thinking if the whole idea had any merit it would be a popular mode by now. Bruce- It has been about 35 years since I had a class in school where SSB-FM was discussed. I recall that if you derive the equations for both AM and FM SSB, they are identical for practical purposes if the FM signal has low deviation (low modulation index?). Looking at Two Meter FM, the deviation typically peaks at about 5 KHz. If you listen to your local repeater with an SSB rig such as the IC-706, it will be obvious that it isn't a clean signal! However, a 3 KHz deviation FM signal on HF (below 29 MHz) will sound much cleaner when tuned as SSB, and you may not notice it isn't AM-SSB. With this in mind, consider that AM-SSB and FM-SSB might just be two ways to generate an SSB signal, assuming you use a filter to eliminate the carrier and other sideband. By the way, an IC-706, especially one with the TCXO, often has a more accurate frequency read-out than a typical Two Meter rig. Therefore you can use it to check a repeater's frequency by tuning it as if it were an SSB station while someone is speaking. It is easy enough to check the IC-706 against WWV on HF. 73, Fred, K4DII |
The amplitudes of the sideband components are symmetrical (at least for
modulation by a single sine wave), but the phases aren't. The phases of all the upper sideband components are in phase with the carrier; in the lower sideband, the odd order components (and only the odd order ones) are reversed in phase. With multitone modulation, things get a whole lot more complex. Unlike AM, FM is nonlinear, so there are sideband components from each tone, plus components from their sum, difference, and harmonics. The inability to use superposition makes analysis of frequency modulation with complex waveforms a great deal more difficult than AM. Note also that unlike AM, whatever fraction of the carrier that's left when transmitting FM also contains part of the modulation information. Of course, at certain modulation indices with pure sine wave modulation, the carrier goes to zero, meaning that all the modulation information is in the sidebands. But this happens only under specific modulation conditions, so you'd certainly have an information-carrying carrier component present when modulating with a voice, for example. Roy Lewallen, W7EL Joel Kolstad wrote: Avery Fineman wrote: There isn't any corresponding similarity of FM and PM to AM for the repetition of sidebands' information when looking at the spectral content. Umm... last I looked the spectrum of FM and PM was symmetrical about the carrier frequency? (Well, the lower sideband is 180 degrees out of phase with the upper, but that's true of AM as well.) Looking at a single sine wave input to an FM or phase modulator, this comes about from the Bessel function expansion of the sidetones and J-n(x)=-Jn(x)? I know you're far more experienced in this area than I am, however, so I'll let you explain what I'm misinterpreting here! ---Joel Kolstad |
The amplitudes of the sideband components are symmetrical (at least for
modulation by a single sine wave), but the phases aren't. The phases of all the upper sideband components are in phase with the carrier; in the lower sideband, the odd order components (and only the odd order ones) are reversed in phase. With multitone modulation, things get a whole lot more complex. Unlike AM, FM is nonlinear, so there are sideband components from each tone, plus components from their sum, difference, and harmonics. The inability to use superposition makes analysis of frequency modulation with complex waveforms a great deal more difficult than AM. Note also that unlike AM, whatever fraction of the carrier that's left when transmitting FM also contains part of the modulation information. Of course, at certain modulation indices with pure sine wave modulation, the carrier goes to zero, meaning that all the modulation information is in the sidebands. But this happens only under specific modulation conditions, so you'd certainly have an information-carrying carrier component present when modulating with a voice, for example. Roy Lewallen, W7EL Joel Kolstad wrote: Avery Fineman wrote: There isn't any corresponding similarity of FM and PM to AM for the repetition of sidebands' information when looking at the spectral content. Umm... last I looked the spectrum of FM and PM was symmetrical about the carrier frequency? (Well, the lower sideband is 180 degrees out of phase with the upper, but that's true of AM as well.) Looking at a single sine wave input to an FM or phase modulator, this comes about from the Bessel function expansion of the sidetones and J-n(x)=-Jn(x)? I know you're far more experienced in this area than I am, however, so I'll let you explain what I'm misinterpreting here! ---Joel Kolstad |
Roy Lewallen wrote:
The amplitudes of the sideband components are symmetrical (at least for modulation by a single sine wave), but the phases aren't. The phases of all the upper sideband components are in phase with the carrier; in the lower sideband, the odd order components (and only the odd order ones) are reversed in phase. I certainly didn't realize that until you pointed it out; I was generalzing from the narrowband FM situation where only the first sideband components are necessarily maintained and incorrectly assuming the same phase differences applied to the general case. However... Say you start with a baseband FM signal. Let's call the two sides of its Fourier transform L and R for the 'left' and 'right' halves. Now we mix up to the desired carrier frequency. At -f_c we have L at even greater negative frequencies and R at smaller negative frequencies. Ditto at f_c. If we now apply a low pass filter to select the lower sideband, we end up with R and L -- No information has been lost! (Likewise, with a high pass filter you have L and R left -- Same deal.) Fundamentally mixing ANY signal followed by SSB filtering shouldn't lose information. Yes, in practice we'll be talking about VSB instead of SSB, but I still think we're OK. Speaking of narrowband FM (NBFM)... and at the risk of splitting this topic... I had a discussion today with someone over the ability to use an envelope detector to recover narrowband FM signals. The output of the envelope detector is approximately 1+0.5*cos^2(2*pi*f*t), where f was the original modulating signal. The '1' will be killed by a capacitor, but that leaves the cosine squared term... which seems impossible to easily change back into cosine, since sqrt(x^2)=abs(x) and therefore it would appear that we've irreversably lost information. Comments? ---Joel Kolstad ....ambitious novice who'll be licensed shortly... ....and I still think C-QUAM AM stereo is quite clever... |
Roy Lewallen wrote:
The amplitudes of the sideband components are symmetrical (at least for modulation by a single sine wave), but the phases aren't. The phases of all the upper sideband components are in phase with the carrier; in the lower sideband, the odd order components (and only the odd order ones) are reversed in phase. I certainly didn't realize that until you pointed it out; I was generalzing from the narrowband FM situation where only the first sideband components are necessarily maintained and incorrectly assuming the same phase differences applied to the general case. However... Say you start with a baseband FM signal. Let's call the two sides of its Fourier transform L and R for the 'left' and 'right' halves. Now we mix up to the desired carrier frequency. At -f_c we have L at even greater negative frequencies and R at smaller negative frequencies. Ditto at f_c. If we now apply a low pass filter to select the lower sideband, we end up with R and L -- No information has been lost! (Likewise, with a high pass filter you have L and R left -- Same deal.) Fundamentally mixing ANY signal followed by SSB filtering shouldn't lose information. Yes, in practice we'll be talking about VSB instead of SSB, but I still think we're OK. Speaking of narrowband FM (NBFM)... and at the risk of splitting this topic... I had a discussion today with someone over the ability to use an envelope detector to recover narrowband FM signals. The output of the envelope detector is approximately 1+0.5*cos^2(2*pi*f*t), where f was the original modulating signal. The '1' will be killed by a capacitor, but that leaves the cosine squared term... which seems impossible to easily change back into cosine, since sqrt(x^2)=abs(x) and therefore it would appear that we've irreversably lost information. Comments? ---Joel Kolstad ....ambitious novice who'll be licensed shortly... ....and I still think C-QUAM AM stereo is quite clever... |
Fred McKenzie wrote:
It has been about 35 years since I had a class in school where SSB-FM was discussed. I recall that if you derive the equations for both AM and FM SSB, they are identical for practical purposes if the FM signal has low deviation (low modulation index?). You're probably thinking of AM vs. narrow band FM. Although the equations look very similar on paper and the MAGNITUDE spectrum is identical, the phase spectrum is different in that -- in the phasor domain -- AM always sits at 0 degrees and just grows and shrinks with modulation (overmodulation pushes it over to 180 degrees, BTW). NBFM, on the other hand, still has the carrier at 0 degrees but grows and shrinks along the imaginary axis. Hence the angle of the phasor is small but time-varying (which implies that the instantaneous frequency is varying as well -- but of course you already knew that since we called this whole mess 'frequency modulation'). The angle is about 15 degrees for a modulation index of 0.3 (what my notes claim as a good cutoff for NBFM) and about 5 degrees at 0.1. See the message I posted earlier tonight for a discussion of whether or not you can recover NBFM with an envelope detector as of course one often does with AM (the difficulty is due to that phasor's wiggling...). I think not, but there's plenty I don't have a clue about... yet! What's the modulation index on two meters anyway? ---Joel Kolstad ....who does know that a wideband FM receiver has no problem whatsoever receiving NBFM... Looking at Two Meter FM, the deviation typically peaks at about 5 KHz. If you listen to your local repeater with an SSB rig such as the IC-706, it will be obvious that it isn't a clean signal! However, a 3 KHz deviation FM signal on HF (below 29 MHz) will sound much cleaner when tuned as SSB, and you may not notice it isn't AM-SSB. |
Fred McKenzie wrote:
It has been about 35 years since I had a class in school where SSB-FM was discussed. I recall that if you derive the equations for both AM and FM SSB, they are identical for practical purposes if the FM signal has low deviation (low modulation index?). You're probably thinking of AM vs. narrow band FM. Although the equations look very similar on paper and the MAGNITUDE spectrum is identical, the phase spectrum is different in that -- in the phasor domain -- AM always sits at 0 degrees and just grows and shrinks with modulation (overmodulation pushes it over to 180 degrees, BTW). NBFM, on the other hand, still has the carrier at 0 degrees but grows and shrinks along the imaginary axis. Hence the angle of the phasor is small but time-varying (which implies that the instantaneous frequency is varying as well -- but of course you already knew that since we called this whole mess 'frequency modulation'). The angle is about 15 degrees for a modulation index of 0.3 (what my notes claim as a good cutoff for NBFM) and about 5 degrees at 0.1. See the message I posted earlier tonight for a discussion of whether or not you can recover NBFM with an envelope detector as of course one often does with AM (the difficulty is due to that phasor's wiggling...). I think not, but there's plenty I don't have a clue about... yet! What's the modulation index on two meters anyway? ---Joel Kolstad ....who does know that a wideband FM receiver has no problem whatsoever receiving NBFM... Looking at Two Meter FM, the deviation typically peaks at about 5 KHz. If you listen to your local repeater with an SSB rig such as the IC-706, it will be obvious that it isn't a clean signal! However, a 3 KHz deviation FM signal on HF (below 29 MHz) will sound much cleaner when tuned as SSB, and you may not notice it isn't AM-SSB. |
Joel Kolstad wrote:
. . . Say you start with a baseband FM signal. Let's call the two sides of its Fourier transform L and R for the 'left' and 'right' halves. Now we mix up to the desired carrier frequency. At -f_c we have L at even greater negative frequencies and R at smaller negative frequencies. Ditto at f_c. If we now apply a low pass filter to select the lower sideband, we end up with R and L -- No information has been lost! (Likewise, with a high pass filter you have L and R left -- Same deal.) Fundamentally mixing ANY signal followed by SSB filtering shouldn't lose information. Yes, in practice we'll be talking about VSB instead of SSB, but I still think we're OK. I'm afraid you lost me with the "baseband" FM signal. Would you provide a carrier frequency, modulation frequency, and deviation or modulation index as an example? The lower and upper sidebands of an FM signal do contain the same information when the modulation is a single sine wave, even though the sidebands aren't identical. But when you modulate with a complex waveform, you might find that some of the information which is adding in one sideband is subtracting in the other, and you might not be able to recover the modulating waveform from only one or the other -- sort of like you can't get two separate stereo channels from just the sum signal. I don't know if that's true, but it wouldn't surprise me. And, as I pointed out in another posting, the entire modulation information isn't even contained in *both* sidebands except under very special conditions -- some is in the carrier. Another question, of course, is whether you can get close enough to be useful. Perhaps with NBFM, at least, you could. Speaking of narrowband FM (NBFM)... and at the risk of splitting this topic... I had a discussion today with someone over the ability to use an envelope detector to recover narrowband FM signals. The output of the envelope detector is approximately 1+0.5*cos^2(2*pi*f*t), where f was the original modulating signal. The '1' will be killed by a capacitor, but that leaves the cosine squared term... which seems impossible to easily change back into cosine, since sqrt(x^2)=abs(x) and therefore it would appear that we've irreversably lost information. Comments? Cos^2(x) = abs(cos(x)) = 1/2 * (1 + cos(2x)). As you've noted, the DC term can be blocked with a capacitor, so you'd end up with a cosine wave at twice the frequency. But I've never heard of trying to detect NBFM directly with an envelope detector like you'd detect AM. The trick we used in ye olden tymes was called "slope detection". You tuned the signal so it was on the edge of the IF filter. The filter slope converted the FM to AM, which was then detected with the normal AM envelope detector. If you tuned directly to the carrier frequency, you didn't hear any modulation to speak of. Roy Lewallen, W7EL |
Joel Kolstad wrote:
. . . Say you start with a baseband FM signal. Let's call the two sides of its Fourier transform L and R for the 'left' and 'right' halves. Now we mix up to the desired carrier frequency. At -f_c we have L at even greater negative frequencies and R at smaller negative frequencies. Ditto at f_c. If we now apply a low pass filter to select the lower sideband, we end up with R and L -- No information has been lost! (Likewise, with a high pass filter you have L and R left -- Same deal.) Fundamentally mixing ANY signal followed by SSB filtering shouldn't lose information. Yes, in practice we'll be talking about VSB instead of SSB, but I still think we're OK. I'm afraid you lost me with the "baseband" FM signal. Would you provide a carrier frequency, modulation frequency, and deviation or modulation index as an example? The lower and upper sidebands of an FM signal do contain the same information when the modulation is a single sine wave, even though the sidebands aren't identical. But when you modulate with a complex waveform, you might find that some of the information which is adding in one sideband is subtracting in the other, and you might not be able to recover the modulating waveform from only one or the other -- sort of like you can't get two separate stereo channels from just the sum signal. I don't know if that's true, but it wouldn't surprise me. And, as I pointed out in another posting, the entire modulation information isn't even contained in *both* sidebands except under very special conditions -- some is in the carrier. Another question, of course, is whether you can get close enough to be useful. Perhaps with NBFM, at least, you could. Speaking of narrowband FM (NBFM)... and at the risk of splitting this topic... I had a discussion today with someone over the ability to use an envelope detector to recover narrowband FM signals. The output of the envelope detector is approximately 1+0.5*cos^2(2*pi*f*t), where f was the original modulating signal. The '1' will be killed by a capacitor, but that leaves the cosine squared term... which seems impossible to easily change back into cosine, since sqrt(x^2)=abs(x) and therefore it would appear that we've irreversably lost information. Comments? Cos^2(x) = abs(cos(x)) = 1/2 * (1 + cos(2x)). As you've noted, the DC term can be blocked with a capacitor, so you'd end up with a cosine wave at twice the frequency. But I've never heard of trying to detect NBFM directly with an envelope detector like you'd detect AM. The trick we used in ye olden tymes was called "slope detection". You tuned the signal so it was on the edge of the IF filter. The filter slope converted the FM to AM, which was then detected with the normal AM envelope detector. If you tuned directly to the carrier frequency, you didn't hear any modulation to speak of. Roy Lewallen, W7EL |
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